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Sharp Energy Estimates for a Class of Weakly Hyperbolic Operators

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New Trends in the Theory of Hyperbolic Equations

Part of the book series: Operator Theory: Advances and Applications ((APDE,volume 159))

Abstract

The intention of this article is twofold: First, we survey our results from [20, 18] about energy estimates for the Cauchy problem for weakly hyperbolic operators with finite time degeneracy at time t = 0. Then, in a second part, we show that these energy estimates are sharp for a wide range of examples. In particular, for these examples we precisely determine the loss of regularity that occurs in passing from the Cauchy data at t = 0 to the solutions.

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  1. Ingo Witt

    Present address: Department of Mathematics, Imperial College, 180 Queen’s Gate, London, SW7 2BZ, UK

Authors and Affiliations

  1. Fachbereich Mathematik und Statistik, Universität Konstanz, D-78457, Konstanz, Germany

    Michael Dreher

  2. Institut für Mathematik, Universität Potsdam, 14415, Potsdam, Germany

    Ingo Witt

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  1. Michael Dreher
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  2. Ingo Witt
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  1. Fakultät für Mathematik und Informatik Institut für Angewandte Analysis, TU Bergakademie Freiberg, 09596, Freiberg, Germany

    Michael Reissig

  2. Institut für Mathematik, Universität Potsdam, 14415, Potsdam, Germany

    Bert-Wolfgang Schulze

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Dreher, M., Witt, I. (2005). Sharp Energy Estimates for a Class of Weakly Hyperbolic Operators. In: Reissig, M., Schulze, BW. (eds) New Trends in the Theory of Hyperbolic Equations. Operator Theory: Advances and Applications, vol 159. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7386-5_6

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